Abstract
Wannier-type threshold theory for multiple break-up processes is based on the existence of special classical trajectories which represent partial fixed points of the equations of motion in a system of charged particles. These trajectories preserve the shape of the initial configuration while only changing its overall size in time. The relation between such scaling configurations and Thomson’s (or surface Coulomb) problem is analyzed. In particular, it is shown that for eight electrons the twisted cube configuration solves Thomson’s problem and also governs the threshold break-up of eight electrons receding from a charged core. The relevant exponents for the threshold power law are evaluated.
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